The conversation went off on a tangent.

谈话突然偏离了正题。

In this paper base tangent length is put forward and lead angle calculating formula is deduced.

这篇文章提出了公法线长度并推导出超前角的计算公式。

It is really the tangent plane.

它确实就是切平面。

That is how we get the tangent plane.

这样我们就得到了切平面。

That's the equation of a tangent plane.

这就是切平面的方程。

And that line is tangent to the surface.

一条与曲面相切的直线。

The direction is tangent to the trajectory.

方向就是轨道的切线方向。

That's one way to define the tangent plane.

这是定义切平面的方法。

We are replacing the graph by its tangent plane.

我们用函数的切平面来替代它的图像。

Going off on a tangent only confuses readers.

写一篇有主题突出的博文，突然转移话题只会让读者感到迷惑。

Then, if I choose any vector in that tangent plane.

那么如果我选择了任何位于切平面的向量。

It's going to be tangent to the level surface, right?

它是与等值面相切的，对不对？

So, it doesn't look very tangent because it crosses the surface.

它看上去并不是十分地相切，因为它穿过了曲面。

That also tells us how to find tangent planes to level surfaces.

这其实也告诉我们，怎样找等值面的切平面。

Let's think about the tangent plane with regard to a function f.

我们来考虑，关于函数f的一个切平面。

It has a hat because it's a unit vector, and t because it's tangent.

这上面有一个帽子表示它是单位矢量，T表示它是切线。

So, the velocity vector is going to be always tangent to the curve.

速度向量总是与曲线相切的。

If we were moving on the tangent plane, this would be an actual equality.

如果我们在切平面上移动，这将会是一个真正的等式。

SVG can turn an image so it always faces the tangent of the line it is following.

SVG可以使图像转向，以便它总是面向它所移动方向的切线。

But, actually, that is not true because here the circle is tangent to the axis.

但实际上，这是不对的，因为这个圆与这个坐标轴相切。

OK, and that's going to be the normal vector to the surface or to the tangent plane.

这就是切平面的，或者说这个曲面的法向量。

Being perpendicular to the surface means that you are perpendicular to its tangent plane.

垂直于曲面也意味着垂直于它的切平面，垂直于曲面也意味着垂直于它的切平面。

That means a magnet has to nudge the protons to enter the circular beam pipe on the tangent.

这意味着必须设置一个磁铁，以便调整质子束方向以保证沿着切向方向导入圆形粒子束管道。

Going on a tangent—as long as it’s one you know the other person will be interested in—really works.

跳出话题，只要是你知道的，对方感兴趣的话题，真的很有效果。

And, at this point, I have the tangent plane to the level surface OK, so this is tangent plane to the level.

在这点上，我们有一个切于等值面的切面，这就是等值面的切平面。

Well, that means the gradient is actually perpendicular to the tangent plane or to the surface at this point.

那意味着，梯度向量在这点上，垂直于切平面或者是等值面。

They are just flowing along the circle around and around so the flux will be zero. F now is tangent to c.

只是沿着曲线流动，所以通量为零，F与C相切。

And now, delta r should be essentially roughly equal to, well, its direction will be tangent to the trajectory.

这里，△r应该是近似等于。。。,它的方向是轨道的切线方向。

If you want strict equalities in approximations means that we replace the function by its tangent approximation.

如果你想要严格的近似等式,那就意味着我们要用切线逼近来取代原函数。